Manifold Geometry with Fast Automatic Derivatives and Coordinate Frame Semantics Checking in C++

TL;DR

This paper introduces wave_geometry, a C++ library that simplifies pose estimation on the SE(3) manifold by providing automatic derivatives and coordinate frame checks, enabling faster and error-free development in robotics and computer vision.

Contribution

The paper presents wave_geometry, a C++ library that combines automatic differentiation with compile-time coordinate frame semantics enforcement for efficient pose computations.

Findings

Evaluates Jacobians with minimal runtime overhead.

Enforces coordinate frame correctness at compile time.

Outperforms existing packages in speed and error prevention.

Abstract

Computer vision and robotics problems often require representation and estimation of poses on the SE(3) manifold. Developers of algorithms that must run in real time face several time-consuming programming tasks, including deriving and computing analytic derivatives and avoiding mathematical errors when handling poses in multiple coordinate frames. To support rapid and error-free development, we present wave_geometry, a C++ manifold geometry library with two key contributions: expression template-based automatic differentiation and compile-time enforcement of coordinate frame semantics. We contrast the library with existing open source packages and show that it can evaluate Jacobians in forward and reverse mode with little to no runtime overhead compared to hand-coded derivatives. The library is available at https://github.com/wavelab/wave_geometry .